Tunable bus-mediated coupling between remote qubits

ABSTRACT

A tunable bus-mediated coupling system is provided that includes a first input port coupled to a first end of a variable inductance coupling element through a first resonator and a second input port coupled to a second end of the variable inductance coupling element through a second resonator. The first input port is configured to be coupled to a first qubit, and the second output port is configured to be coupled to a second qubit. A controller is configured to control the inductance of the variable inductance coupling element between a low inductance state to provide strong coupling between the first qubit and the second qubit and a high inductance state to provide isolation between the first qubit and the second qubit.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of and claims priority to co-pendingU.S. patent application No. 15/003232, filed 21 Jan. 2016, which isincorporated herein in its entirety.

GOVERNMENT INTEREST

This invention was made with Government support under Contract No.30059298. The Government has certain rights in this invention.

TECHNICAL FIELD

The present invention relates generally to superconducting circuits, andmore particularly to tunable bus-mediated coupling between remotequbits.

BACKGROUND

The fundamental challenge for quantum computation and simulation is toconstruct a large-scale system of highly connected coherent qubits toperform various operations. Superconducting qubits utilize macroscopiccircuits to process quantum information and are a promising candidatetowards this end. Recently, materials research and circuit optimizationhas led to significant progress in qubit coherence. Superconductingqubits can now perform hundreds of operations within their coherencetimes, allowing for research into complex algorithms such as errorcorrection. In many applications, it is desirable to combine thesehigh-coherence qubits with tunable inter-qubit coupling, since it wouldallow for both coherent local operations and dynamically varying qubitinteractions. For quantum computation, this would provide isolation forsingle-qubit gates while at the same time enabling fast two-qubit gatesthat minimize errors from decoherence. Despite previous attempts attunable coupling, these applications have yet to be realized due to thechallenge of incorporating tunable, long-distance coupling with highcoherence devices.

SUMMARY

In one example, a tunable bus-mediated coupling system is provided thatincludes a first input port coupled to a first end of a variableinductance coupling element through a first resonator and a second inputport coupled to a second end of the variable inductance coupling elementthrough a second resonator. The first input port is configured to becoupled to a first qubit, and the second output port is configured to becoupled to a second qubit. A controller is configured to control theinductance of the variable inductance coupling element between a lowinductance state to provide strong coupling between the first qubit andthe second qubit and a high inductance state to provide isolationbetween the first qubit and the second qubit.

In another example, a superconducting system is provided that comprisesa first qubit system having a first qubit, and a second qubit systemremote from the first qubit system and having a second qubit. A tunablebus-mediated coupler is disposed between the first qubit and the secondqubit. The tunable bus-mediated coupler has a first state for stronglycoupling the first qubit to the second qubit and a second state forisolating the first qubit from the second qubit.

In yet a further example, a superconducting system is provided thatcomprises a first qubit system comprising a first qubit, a second qubitsystem remote from the first qubit system and comprising a second qubit,and a tunable bus-mediated coupler disposed between the first qubit andthe second qubit, The tunable bus-mediated coupler comprises a firstinput port coupled to a first end of a Josephson junction through afirst resonator and a second input port coupled to a second end of theJosephson junction through a second resonator. The first input port iscoupled to the first qubit and the second output port is coupled to thesecond qubit. The tunable bus-mediated coupler comprises a firsttermination inductor coupled between the first resonator and theJosephson junction on a first end and ground on a second end, and asecond termination inductor coupled between the second resonator and theJosephson junction on a first end and ground on a second end, whereinthe first termination inductor, the Josephson junction and the secondtermination inductor form an RF-Squid. A bias inductor is inductivelycoupled to one of the first termination inductor and the secondtermination inductor, wherein an amount of current through the biasinductor controls the coupling strength between the first and the secondqubit. A controller controls an amount of current through the biasinductor inductively coupled to one of the first and the secondtermination inductors to control the inductance of the Josephsonjunction between a low inductance state to provide strong couplingbetween the first qubit and the second qubit and a high inductance stateto provide isolation between the first qubit and the second qubit.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a block diagram of an example of a superconductingsystem.

FIG. 2 illustrates a schematic of an example of a tunable bus-mediatedcoupler that could be employed in FIG. 1.

FIG. 3 illustrates a graph of the voltage along the length of combinedcoupled-resonator system showing the even (dashed) and odd (solid) modesof oscillation.

FIG. 4 is a schematic level diagram showing the hybridized left andright resonators of FIG. 2 producing frequency-split even and odd modes

FIG. 5 illustrates a graphical panel showing results of a simulation fora particular flux setting.

FIG. 6 illustrates a graphical panel showing the frequency splitting ofthe even and odd bus modes due to the flux-dependent coupling.

FIG. 7 illustrates a graph of simulation results showing the dependenceof the bus mode splitting and the qubit-qubit bus-mediated coupling as afunction of the junction flux-dependent critical current.

DETAILED DESCRIPTION

The present disclosure relates generally to superconducting circuits,and more particularly to tunable bus-mediated coupling (or coupler)between remote qubits. In one example, a variable inductance couplingelement is placed between two qubits that may reside in separate remotesuperconducting systems. The variable inductance coupling element can beadjusted between a strongly coupled state and a decoupled (or isolation)state between qubits in addition to various states of intermediatecoupling strengths in between. In this manner, manipulation can beperformed on state information of isolated qubits in a decoupled state,while this state information can be exchanged between qubits during astrongly coupled state. Furthermore, state information can bemanipulated and passed between qubits without destroying the stateinformation of the originating qubit in an intermediate couplingstrength state between qubits. In one example, the variable inductancecoupling element can be a Josephson junction. A variable inductancecoupling element can be arranged as a single Josephson junction orseries array of N Josephson junctions, each having a critical current Ntimes larger than the original Josephson junction.

In another example, an RF-SQUID tunable coupler includes a Josephsonjunction embedded in the middle of a half-wave resonator bus. TheRF-SQUID facilitates bus-mediated dispersive interaction between thequbits for coupling. The advantage of bus-mediated coupling is that thequbits can be physically placed remotely from each other, for example,in separate circuit blocks on the quantum processor chip. The advantageof a tunable coupler, which can essentially be turned off when desired,is a reduction in frequency crowding and unwanted residual interactionsbetween the qubits. Furthermore, the interaction strength can becalibrated and trimmed in the field to compensate for variability in themanufacturing process, and can be controlled in real time as part of thecomputation protocol.

The Josephson junction can have a first inductance when no current or alow current is induced in the SQUID, and a second inductance when acurrent or a higher current is induced in its respective SQUID that isat a predetermined threshold that generates or induces a flux, forexample, greater than about 0.1 Φ₀ and less than about 0.45 Φ₀, where Φ₀is equal to a flux quantum. The first inductance (e.g., ℏ/2e * 1/I_(C),where ℏ is Planck's constant divided by 2π, e is electron charge andI_(C) is the critical current of the Josephson junction) can providecoupling between the first and second qubits. The second inductance(e.g., large inductance value) can provide decoupling between the firstand second qubits.

FIG. 1 illustrates a block diagram of an example of a superconductingsystem 10. The superconducting system includes a first qubit system 12coupled to a second qubit system 16 through a tunable coupler system 14.The first qubit system 12 includes a plurality of qubits labeled, qubit(1,1) to qubit (1,N), and the second qubit system 16 includes aplurality of qubits labeled, qubit (2,1) to qubit (2,N), such that (X,N)provides X which represents the qubit system and N represents a qubitnumber within the qubit system, where N is an integer greater than orequal to one. The first qubit system 12 and the second qubit system 16can be separate logical blocks that perform different logical operationssuch as different gate operations, error correction operations, memoryoperations, or any of a variety of other superconducting operations. Thefirst qubit system 12 and second qubit system 16 can also includevarious additional qubits and other superconducting elements that arenot coupled to qubits in the other qubit system, but may be coupled toother qubits in its respective system for performing a variety of qubitand other superconducting operations.

Each qubit in the first qubit system 12 is coupled to a respective qubitin the second qubit system 16 by a respective tunable coupler of thetunable coupler system 14 having N tunable couplers, labeled tunablecoupler 1 through tunable coupler N. Each tunable coupler includes avariable inductance coupling element that can be adjusted to allow forcontrol of the coupling strength between two independent qubits of theopposing qubit systems 12 and 16, respectively. The variable inductancecoupling element can be disposed between two resonators to allow forremote coupling of the two independent qubits via a tunable bus-mediatedcoupler. In one example, the variable inductance coupling element is aJosephson junction that resides in a RF SQUID disposed between tworesonators. The superconducting switching system 10 also includes aswich controller 18 and bias elements 16. The variable inductancecoupling elements are controlled by magnetic flux via the bias elements16 and the switch controller 18 to couple, decouple and to control thecoupling strength of the coupling between respective independent qubitsin opposing qubit systems 12 and 16.

FIG. 2 illustrates a schematic of an example of a tunable bus-mediatedcoupler 30 that could be employed in FIG. 1. The tunable bus-mediatedcoupler 30 is composed of a first quarter-wave transmission lineresonator TL1 and a second quarter-wave transmission line resonator TL2.A first coupling capacitor C1 couples a first port (Port 1) to a firstend of the first quarter-wave transmission line resonator TL1, and asecond coupling capacitor C2 couples a second port (Port 2) to a firstend of the second quarter-wave transmission line resonator TL2. Thefirst port (Port 1) can be coupled to a first qubit and the second port(Port 2) can be coupled to a second qubit. A second end of the firstquarter-wave transmission line resonator TL1 is shorted to ground via afirst terminating inductor (L1) and a second end of the secondquarter-wave transmission line resonator TL2 is shorted to ground via asecond terminating inductor L2. A Josephson junction (J1) is furtherconnected between the termination inductors L1 and L2, so that theJosephson junction J1 together with termination inductors L1 and L2,form an RF-SQUID 32.

The RF-SQUID 32 functions as a variable transformer, controlled by amagnetic flux Φ_(e), induced in the RF-SQUID loop via a mutualinductance M induced by a current flowing between a third port (Port 3)and a fourth port (Port 4) through a bias inductance L3. When the fluxenclosed in the RF-SQUID 32, Φ_(e), is an appreciable fraction of Φ₀/2,as determined by the ratio of the Josephson junction J1 to linearinductances L1 and L2 in the RF-SQUID 32, the effective mutual couplingbetween the two resonators TL1 and TL2 is essentially zero. When theenclosed flux is close to zero or an integer multiple of Φ₀, theeffective mutual coupling between the resonators TL1 and TL2 isappreciable, and equals to M_(eff)=L₁*L₂/(L_(J1)+L₁+L₂). Close to anenclosed flux of Φ₀/2, the effective mutual coupling is appreciable andnegative. Therefore, the effective mutual coupling M_(eff)(Φ_(e))between the two resonators TL1 and TL2 is a function of the appliedflux. The flux can be varied between zero and Φ₀/2 by changing thecurrent through bias inductance L3 to provide varying strengths of theeffective coupling between the first and second qubits coupled to thefirst port (Port 1) and the second port (Port 2), respectively.

FIG. 3 illustrates a graph 40 of the voltage along the length ofcombined coupled-resonator of FIG. 2 showing the even (dashed) and odd(solid) modes of oscillation. Because of the coupling between the twotransmission line resonators TL1 and TL2, the combined system exhibittwo oscillating eigen-modes having different frequencies. A first oddmode having a frequency Ω_(o) close to the half-wave frequency of thecombined system, and in which the voltages at the ends of thetransmission lines oscillate 180 degrees out of phase, and an even modehaving a different frequency Ω_(e) in which the voltages at the ends ofthe transmission lines oscillate in phase. When the coupling ispositive, the even mode frequency is greater than the odd modefrequency. When the coupling is negative, the even mode frequency islower than the odd mode. In either case the even and odd modes are splitin frequency by an amount 2g_(c), proportional to the effective mutualM_(eff)(Φ_(e)).

Qubits that are connected to the two ports of the coupled-resonator busvia capacitors C1 and C2 of FIG. 2, each interact with both even and oddmodes of the bus. In the dispersive regime, when the qubit frequenciesare sufficiently detuned from the bus frequencies, an effectivebus-mediated interaction between the qubits exists. However, the sign ofthe mediated interaction due to the even mode is opposite to that of theinteraction due to the odd mode, and therefore the total effectivemediated coupling can be determined as a balance of the coupling due tothe two bus modes. In particular, the two contributions can be madeequal in magnitude and opposite in sign, resulting in a cancellation ofthe coupling. FIG. 4 is a schematic level diagram 50, showing thehybridized left and right resonators producing the frequency-split evenand odd modes, and the left and right qubits each at a respectivedetuning Δ_(L,Ro) from the odd mode, and Δ_(L,Re) from the even mode.

The overall bus-mediated coupling between the qubits in the dispersiveregime, g_(eff), as a function of the detuning is given by:

$\begin{matrix}{g_{eff} = {\frac{g_{L}g_{R}}{2}\left( {\frac{1}{\Delta_{Le}} + \frac{1}{\Delta_{Re}} - \frac{1}{\Delta_{Lo}} - \frac{1}{\Delta_{Ro}}} \right)}} & {{EQUATION}\mspace{14mu} 1}\end{matrix}$

where g_(L,R) are the fixed coupling strengths of the qubit to therespective resonators via capacitors C1 and C2 in FIG. 2. When thefrequencies of the two qubits are equal so that Δ_(Le)=Δ_(Re)=Δ_(e) andΔ_(Lo)=Δ_(Ro)=Δ_(o), the expression for the effective bus-mediatedqubit-qubit coupling simplifies to:

$\begin{matrix}{g_{eff} = {g_{L}{g_{R}\left( \frac{2g_{c}}{\Delta_{e}\Delta_{o}} \right)}}} & {{EQUATION}\mspace{14mu} 2}\end{matrix}$

where g_(eff) is dependent on the flux Φ_(e) via g_(c) and, implicitly,via Δ_(e) and Δ_(o), which are all flux-dependent.

An Agilent's Advanced Design Simulation (ADS) tool simulation wasperformed with the junction approximated with a linear inductor whosevalue was changed from the nominal zero-current Josephson inductance upto a value 50 times greater. The results of the simulation for aparticular flux setting are shown in a panel 60 of FIG. 5 showing thesplitting in the qubit spectrum due to the effective interactiong_(eff), and a panel 70 of FIG. 6 showing the frequency splitting of theeven and odd bus modes due to the flux-dependent coupling g_(c). Thesimulations confirm the functional dependence of g_(eff) on g_(c), andconfirm the expected dependence of g_(c) on the flux-tunable inductanceof the Josephson junction.

FIG. 7 illustrates a graph 80 of simulation results showing thedependence of the bus mode splitting g_(c) and the qubit-qubitbus-mediated coupling g_(eff) as a function of the junctionflux-dependent critical current for a certain value of the qubit-busfrequency detuning. While in the examples shown, the bus frequency ishigher than the qubit frequencies, the same behavior is replicated whenthe bus frequency is lower than the qubit frequencies.

To summarize, an RF-SQUID tunable coupler embedded between two quarterwave resonators such that the combined system forms a quantum bus havingtwo modes that contribute with opposite signs to a mediated qubit-qubitinteraction. The total effective interaction between the qubits is thustunable with flux as a balance between the contributions to the mediatedcoupling from the two bus modes. The advantage of a tunable coupling,which can essentially be turned off when desired, is a reduction infrequency crowding and unwanted residual interactions between thequbits. Furthermore, the interaction strength can be calibrated andtrimmed in the field to compensate for variability in the manufacturingprocess, and can be controlled in real time as part of the computationprotocol.

What have been described above are examples of the invention. It is, ofcourse, not possible to describe every conceivable combination ofcomponents or methodologies for purposes of describing the invention,but one of ordinary skill in the art will recognize that many furthercombinations and permutations of the invention are possible.Accordingly, the invention is intended to embrace all such alterations,modifications, and variations that fall within the scope of thisapplication, including the appended claims.

What is claimed is:
 1. A tunable bus-mediated coupling systemcomprising: a first port coupled to a first end of a variable inductancecoupling element through a first resonator, the first port beingconfigured to be coupled to a first qubit; a second port coupled to asecond end of the variable inductance coupling element through a secondresonator, the second port being configured to be coupled to a secondqubit; and a controller configured to control the inductance of thevariable inductance coupling element between a low inductance state toprovide strong coupling between the first qubit and the second qubit anda high inductance state to provide isolation between the first qubit andthe second qubit.
 2. The system of claim 1, wherein the variableinductance coupling element comprises a series array of N Josephsonjunctions, each having a critical current N times larger than a singleJosephson junction.
 3. The system of claim 1, wherein the variableinductance coupling element is a Josephson junction.
 4. The system ofclaim 3, further comprising a first termination inductor coupled betweenthe first resonator and the Josephson junction on a first end and groundon a second end, and a second termination inductor coupled between thesecond resonator and the Josephson junction on a first end and ground ona second end, wherein the first termination inductor, the Josephsonjunction and the second termination inductor form an RF-SQUID.
 5. Thesystem of claim 4, further comprising a bias inductor inductivelycoupled to one of the first termination inductor and the secondtermination inductor, wherein an amount of current through the biasinductor controls the coupling strength between the first and the secondqubit.
 6. The system of claim 4, further comprising a first couplingcapacitor coupled between the first port and the first resonator, and asecond coupling capacitor coupled between the second port and the secondresonator.
 7. The system of claim 5, wherein the controller controls anamount of current through the bias inductor inductively coupled to oneof the first and the second termination inductors.
 8. The system ofclaim 7, wherein the controller provides a current through the biasinductor between no current that induces no net flux in the RF-SQUIDallowing for coupling between the first and second qubit and a currentthat induces a net flux in the RF-SQUID of about 0.1 Φ₀ to about 0.45Φ₀, where Φ₀ is equal to a flux quantum, providing isolation between thefirst and second qubit.
 9. A superconducting system comprising thetunable bus-mediated coupling system of claim 1, the superconductingsystem comprising a first qubit system comprising the first qubit, and asecond qubit system remote from the first qubit system and comprisingthe second qubit, wherein the tunable bus-mediated coupling system isarranged to couple and decouple the first qubit and second qubit.
 10. Asuperconducting system comprising: a first qubit system comprising afirst qubit; a second qubit system remote from the first qubit systemand comprising a second qubit; and a tunable bus-mediated couplerdisposed between the first qubit and the second qubit, the tunablebus-mediated coupler having a first state for strongly coupling thefirst qubit to the second qubit and a second state for isolating thefirst qubit to the second qubit.
 11. The system of claim 10, wherein thetunable bus-mediated coupler comprises a variable inductance couplingelement disposed between a first resonator coupled to the first qubitand a second resonator coupled to the second qubit.
 12. The system ofclaim 11, further comprising a controller configured to control theinductance of the variable inductance coupling element between a lowinductance state to provide strong coupling between the first qubit andthe second qubit and a high inductance state to provide isolationbetween the first qubit and the second qubit.
 13. The system of claim11, wherein the variable inductance coupling element is a Josephsonjunction.
 14. The system of claim 13, further comprising a firsttermination inductor coupled between the first resonator and theJosephson junction on a first end and ground on a second end, and asecond termination inductor coupled between the second resonator and theJosephson junction on a first end and ground on a second end, whereinthe first termination inductor, the Josephson junction and the secondtermination inductor form an RF-SQUID.
 15. The system of claim 14,further comprising a bias inductor inductively coupled to one of thefirst termination inductor and the second termination inductor, whereinan amount of current through the bias inductor controls the couplingstrength between the first and the second qubit.
 16. The system of claim15, further comprising a first coupling capacitor coupled between thefirst qubit and the first resonator, and a second coupling capacitorcoupled between the second resonator and the second qubit.
 17. Thesystem of claim 15, wherein the controller provides a current throughthe bias inductor between no current that induces no net flux in theRF-SQUID allowing for coupling between the first and second qubit and acurrent that induces a net flux in the RF-SQUID of about 0.1 Φ₀ to about0.45 Φ₀, where Φ₀ is equal to a flux quantum, providing isolationbetween the first and second qubit.
 18. A superconducting systemcomprising: a first qubit system comprising a first qubit; a secondqubit system remote from the first qubit system and comprising a secondqubit; and a tunable bus-mediated coupler disposed between the firstqubit and the second qubit, the tunable bus-mediated coupler comprising:a first port coupled to a first end of a Josephson junction through afirst resonator, the first port being coupled to the first qubit; asecond port coupled to a second end of the Josephson junction through asecond resonator, the second port being coupled to the second qubit; afirst termination inductor coupled between the first resonator and theJosephson junction on a first end and ground on a second end, and asecond termination inductor coupled between the second resonator and theJosephson junction on a first end and ground on a second end, whereinthe first termination inductor, the Josephson junction and the secondtermination inductor form an RF-SQUID; a bias inductor inductivelycoupled to one of the first termination inductor and the secondtermination inductor, wherein an amount of current through the biasinductor controls the coupling strength between the first and the secondqubit; and a controller that controls an amount of current through thebias inductor inductively coupled to one of the first and the secondtermination inductors to control the inductance of the Josephsonjunction between a low inductance state to provide strong couplingbetween the first qubit and the second qubit and a high inductance stateto provide isolation between the first qubit and the second qubit. 19.The system of claim 18, further comprising a first coupling capacitorcoupled between the first qubit and the first resonator, and a secondcoupling capacitor coupled between the second resonator and the secondqubit.
 20. The system of claim 18, wherein the controller provides acurrent through the bias inductor between no current that induces no netflux in the RF-SQUID allowing for coupling between the first and secondqubit and a current that induces a net flux in the RF-SQUID of about 0.1Φ₀ to about 0.45 Φ₀, where Φ₀ is equal to a flux quantum, providingisolation between the first and second qubit.